Question about deflection of light test

I've always been fascinated by Einstein’s theories about the speed of light and have always wondered about something that I've never been able to find the answer to. Any books I read were either too simple and did not address my question or too complex that I didn't understand it.

It's time I put this question forward in the hopes that someone will be able to answer it in terms I understand.

It’s in regards to Einstein’s deflection of light by the Sun test. From what I understand, using his equations, he calculated how much the sun would bend light before it could be tested. When it could be tested it was found to be correct and when normal geometry (not sure of the correct term) was used that answer was wrong.

My question is: What did they use for the speed of light when they tried normal geometry equations?

This has been bothering me for awhile. I’ll explain why after I receive an answer.

It doesn't. GR predicted spacetime curvature. It still does. Photons are massless particles traveling through spacetime. Spacetime bends, photons do not. Not liking it is optional. This is an exercise in futility.

This 'Newtonian' component in the GR calculation, mentioned above, is the remaining part of the curvature of space-time i.e. that due to time dilation, equal to the Newtonian 'acceleration' on the photon at each part of its trajectory. It is this component that is described by the Einstein Equivalence Principle, "photons fall towards the Sun at the same rate as all particles".

I don't understand all of your post but I see that C is used in the Newtonian equation so now we come to why I asked the question in the first place.

First a little history. From what I understand of Einstein’s formulas, he started with 2 assumptions;
1. Any observer moving at a constant speed would have the same laws of physics.
2. The speed of light c is always constant, no matter how fast or in what direction the light source was moving.

Or as I like to say; everything is relative except light.

First of all I have a problem with that. Why should light be different than everything else in the universe? But let’s move on.

Einstein then did some calculations and found that light can’t be a constant because it causes contradictions in his calculations and of course we know it is counterintuitive.

But, being the great mathematician that he is, he took on the challenge to find a way to make it work and in the end he did it by making space, mass and time malleable. In other words to make one counterintuitive fact true (that light is constant) he had to introduce another 3 counterintuitive elements (namely that space, mass and time are malleable).

Now we come back to the bending light experiment and its apparent result supporting Einstein’s theories. If you are trying to prove Einstein’s formulas you are actually trying to prove his original assumption (that the speed of light is a constant). After all the formulas directly came about because of that assumption.

Would it then not make sense that if you are trying to see what answer you would get with Newtonian formulas you should not be using his constant value for the speed of light? Only Einstein’s formula was created to cater for that constant value. There is no place for it in Newtonian logic.

I think early on scientists took it so much for granted that when doing calculations they used C with and without Einstein’s formulas without thinking and so of course it seemed that only Einstein’s formulas came up with the correct answer.

I suspect and put forward for anyone who can do the calculations, that if you used a variable speed of light with the Newtonian formulas you may well also get the correct answer with the bending light test and possibly with others.

So if I’m correct, on one hand we would have a counterintuitive assumption and 3 counterintuitive changes to our understanding of space, mass and time and on the other hand we would have light acting just like everything else in the universe and everything else behaving the way we feel it should.

Now, all that remains is to apply one swift swipe with Occam’s Razor to see what remains.

Or maybe I'm just showing my ignorance. Please feel free to correct any errors in my understanding and keep any explanations at this layman level or I problably wont understand it. Thanks.

I think early on scientists took it so much for granted [...] without thinking [...]

I suspect and put forward for anyone who can do the calculations, that if you used a variable speed of light with the Newtonian formulas you may well also get the correct answer with the bending light test and possibly with others.

So if I’m correct [...] all that remains [sic] is to apply one swift swipe with Occam’s Razor [...] Or maybe I'm just showing my ignorance.

Look, yes, you're just showing your ignorance. It's a bit rude to accuse so many scientists of not thinking, you should first try to understand what it really means to be a scientist and second study the history of relativity theory.

Relativity is a simple theory (in the sense that it can be defined with just a few short axioms), its predictions have been surprising and nonetheless verified to high precision. You're suggesting that a completely different theory might make a couple of the same predictions. Who cares, unless it can make all of the same predictions plus get something new correct (something that relativity gets wrong)? Your theory certainly isn't simpler yet, since you still need to arbitrarily specify how the speed changes. And worse, you haven't even bothered to complete your theory (nor state a specific prediction), and already you're criticising the mainstream theory!

I suggest you sit in on some university level courses, and learn the mainstream theory. It is "crackpot" behaviour to propose your own new theories before you even know how to scientifically compare the theories' merit.

Special relativity says that the speed of light at the observer's own location is fixed, and this has been confirmed to very high precision by experiment, to the point that it is now fixed by definition, and so units of length and time now have a fixed relationship. (The original question as to whether the speed of light is fixed is therefore now replaced by a question as to whether the size of the metre is constant).

However, the speed of light at a remote location is a matter of choosing your definitions. If you try to map gravitational effects on to a flat Euclidean coordinate system, you will find that the local speed of light relative to that coordinate system depends on the potential, and may even depend on the direction. If you choose an "isotropic" coordinate system (where the ratio of the local ruler size to the corresponding spatial coordinate is the same in all directions, which is for example known to be possible in a spherically symmetrical potential) then you can calculate the effects of gravity on light and orbits by treating the speed of light as a scalar variable which is a function of the potential. When the appropriate function is used for the potential to match General Relativity, the usual GR expressions are obtained for the deflection of light and (more sensitively) the precession of orbits.

The first-order approximation is that the coordinate c varies as (1 - 2GM/rc^2), so the fractional change is twice the Newtonian potential. For calculating the precession of orbits accurately, it is necessary to use the correct second-order term in (GM/rc^2)^2 as well.

This method of calculating using a variable scalar c is limited to the special case of isotropic coordinate systems. In more general cases, the speed of light relative to the coordinate system varies with direction, and calculations are usually performed using tensors instead.

First of all I have a problem with that. Why should light be different than everything else in the universe? But let’s move on.
..................

No don't “move on”
because in the context you say "every thing is relative" you are incorrect to say 'except light'.

All observers follow the same rules of physics; include how they observe light. No Except about it.

All observers use the same physics to find the new speed in there own reference frame of anything (including light) send at v1 from a reference frame moving at v2 .
That correct physics is:
vtotal = (v1 + v2) / (1 + v1 v2/cc)

When you say 'except light' what rules do you think light is not following?
Not this one; if v1 is “c” how is vtotal going to be anything but “c” as well? Use and refrance frame speed you want 0.1c. 0.5c even 1.0c or the impossible referance frame speed of 1.1c (which in fact Hubble did find)! Light speed will still total 1.0c as SR demands.

Before you “move on” to GR, do what you can to be sure you understand SR.

I thought Einstein’s second assumption was that light would always appear to be moving at speed C regardless of the frame of reference and this caused contradictions unless time, space and mass were made malleable.

So would they have used a constant value for the speed of light, namely C, with the bending light test when doing the calculations using Einstein’s formulas and a variable speed of light with the Newtonian formulas because the particles of light would be speeding up as they approached the sun and slowing down as they moved away? Or doesn’t the speed of light come into it? Or have I misunderstood it completely?

So would they have used a constant value for the speed of light, namely C, with the bending light test when doing the calculations using Einstein’s formulas and a variable speed of light with the Newtonian formulas because the particles of light would be speeding up as they approached the sun and slowing down as they moved away? Or doesn’t the speed of light come into it? Or have I misunderstood it completely?

The Newtonian argument simply follows from the "Principle of equivalence" which says that gravity is locally the same as acceleration, so one would expect light beams in a box subjected to a gravitational field to behave in the same way as light beams in a box which is being accelerated upwards in the absence of a field. From this, one would expect light travelling past the sun to be accelerated in exactly the same way as a material object would be.

That basic argument assumes that space itself is unaffected by gravity, but from Einstein's equations we find that relative to some "flat" rectangular coordinate system, space as measured by local rulers "shrinks" in a deeper gravitational potential, so it is in a sense slightly more "dense" closer to the sun, and light therefore travels more slowly, as if travelling through a medium with an increased refractive index. This means that light passing the sun (or a material object travelling at near the speed of light) is deflected by exactly twice as much as would be predicted from the simple Newtonian acceleration. This has of course been confirmed by experiment.

This might suggest that a horizontal light beam within a box would be accelerated downwards twice as much as a material object. It is indeed accelerated downwards by twice the Newtonian acceleration relative to the flat coordinate system. However, the local horizontal spatial coordinates in a gravitational field appear to be slightly curved downwards relative to the background flat coordinate system, by an amount which is equivalent to the usual Newtonian acceleration when travelling horizontally at c, and the vertical coordinates (the sides of the box) converge slightly in a downwards direction. Relative to those local curved coordinates, a fast-moving object accelerates downwards only by the usual Newtonian acceleration, so in the local view the acceleration does not depend on the speed and observations are consistent with the Principle of Equivalence.

How far do you intend to progress, depending on other people to interpret every step of the way? I suggest you get a first year undergraduate physics textbook (like Tipler), some high school maths textbooks, and work towards being able to understand some of this material properly for yourself. (After that you would do the exercises in Rindler's SR book, then start on a GR textbook. Finally, you need to thoroughly research important experimental results, not just one or two.)

because the particles of light would be speeding up as they approached the sun and slowing down as they moved away? Or doesn’t the speed of light come into it? Or have I misunderstood it completely?

I think you are being badly confused because none of the participants in the discussion are being sufficiently precise in describing what theory and what simplifying assumptions they have in mind when they say this or that. Even worse, you insist upon the following terribly misguided principle:

I like to define mathematics as the art of reasoning about simple phenomena without getting confused. Without its assistance, even simple phenomena confuse humans. This is why mathematics is essential for understanding physics. You really can't expect to understand much in physics without being able to follow the math.

(Advanced students may recognize that one issue I have in mind here is that we are discussing various approximations and idealizations which are introduced in order to simply the mathematical discussion of various physical effects. And with experience one recognizes that making useful approximations and idealizations are just where the greatest skill is required in physics. One might even say that this is the "physical" part of physics; once appropriate approximations have been made, purely mathematical reasoning comes into play.)

You know, from a quite natural point of view, light slows down near the sun (as it would in a converging refractive lense).

Case in point: at a guess, Cesium is thinking of the "Shapiro light delay effect" in gtr, one of the four classical solar system tests of gtr (one of the others is the "light bending effect").

The trouble is that neither you nor he were careful to note that there are multiple operationally significant notions of "distance in the large" in curved spacetimes, nor that these are in turn distinct from "coordinate speeds". In simple terms, this means that in curved spacetime models, coordinate speeds have no geometric or physical meaning; to obtain a notion of distance in the large and thus speed in the large which has operational significance in the sense that it can be experimentally tested, you need to specify a method of measurement and a method for computing a "distance" from those measurements.

The Shapiro effect is based upon one of the simplest notions of distance in the large, called radar distance, and then one can show that gtr predicts a "time delay" for signals passing near a massive object. This has been tested many times, and so far the gtr prediction has been confirmed by each test.

This does not contradict that fact that the speed of light is constant; you just have to understand what "the speed of light means".

How far do you intend to progress, depending on other people to interpret every step of the way? I suggest you get a first year undergraduate physics textbook (like Tipler), some high school maths textbooks, and work towards being able to understand some of this material properly for yourself. (After that you would do the exercises in Rindler's SR book, then start on a GR textbook. Finally, you need to thoroughly research important experimental results, not just one or two.)

Ditto. You either need to take our word for it (in particular, to take our word for it that we are not contradicting ourselves when we write down a formula for the Shapiro light delay in which the symbol "c" appears), or else master enough math to follow along with a good textbook. I think D'Inverno is a very readable textbook, by the way.

Using local clocks and rulers, light does not speed up or slow down as it approaches or leaves a large mass, though it does gain (in the former case) or lose (in the later case) energy and momentum.

However, the clocks and rulers themselves can be said to change, i.e. due to gravitational time dilation. The speed of light is only constant when measured using local clocks and rulers.

The other subtle point to remember is that from a fixed reference point some distance away from the sun does see the light passing very near the sun Slow Down not speed up.
Because relative to that point the local clocks near the sun are running slower.
Radar tests that have proven this experimentally as one of the several proofs for GR you will find.